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Unit Normal for Epicycloid

  1. Nov 19, 2015 #1
    Hi Folks,

    I got stuck towards the end where it ask to derive the unit normal (eqn 3.2.29 I don't know how they arrived at [tex]n_x[/tex]. I have looked at trig identities....and I have assumed the following


    I dont see the (r+p) term anywhere in neither the top nor bottom.

    PS: I have posted this in MHB on Tues but no response.


    Attached Files:

  2. jcsd
  3. Nov 19, 2015 #2


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    The norm of the normal vector is ##|\mathbf{N}| = \sqrt{ N_x^2 + N_y^2 }##. The unit normal is ##\mathbf{n} = \mathbf{N}/ |\mathbf{N}|##, so
    $$ n_x = \frac{ N_x}{\sqrt{N_x^2 + N_y^2}}.$$
    In particular, there are common factors of ##r+\rho## in the numerator and denominator that cancel out. The rest of the simplification of the denominator can be accomplished with some trig identities.
  4. Nov 20, 2015 #3
    Ok, great thanks. I should work it out now.
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